Consider the region in the first quadrant of the xy-plane bounded by the graphs
ID: 2892162 • Letter: C
Question
Consider the region in the first quadrant of the xy-plane bounded by the graphs of y = 1 + Squareroot x, y = 2, and x = 9. The region is shaded in the graph below. (a) Set up integral to calculate the area of integrating with respect to y-(Do not integral.) (b) Set up an integral to the volume of the solid resulting from revolving this region around the line y = 1 using the disk/whaler method. (Do not evaluate the integral.) (c) Set up an integral to calculate the volume of the solid resulting from revolving this region around the line y = 1 using the shell method. (Do not evaluate the integral.)Explanation / Answer
given curves y=1+x , y =2 , x=9
a)
y=1+x
=>x=y-1
=>x=(y-1)2
x=(y-1)2 , x=9
=>(y-1)2 =9
=> y-1 =3
=>y =4
2y4
area of the region = 24 [9-(y-1)2] dy
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b)
y=1+x , y =2
1+x =2
=>x =1
=>x =1
1x9
inner radius =2-(-1) =3
outer radius = (1+x)-(-1)=2+x
volume about y =-1 using washer method,V=19[(2+x)2-32] dx
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c)x=(y-1)2 , x=9, 2y4
radius of shell =1+y
height of shell = 9-(y-1)2
volume about y =-1 using shell method,V=24 2(1+y)(9-(y-1)2) dy